On the Crossing Numbers of Complete Graphs

dc.contributor.author	Pan, Shengjun	en
dc.date.accessioned	2006-08-22T14:26:51Z
dc.date.available	2006-08-22T14:26:51Z
dc.date.issued	2006	en
dc.date.submitted	2006	en
dc.description.abstract	In this thesis we prove two main results. The Triangle Conjecture asserts that the convex hull of any optimal rectilinear drawing of <em>K<sub>n</sub></em> must be a triangle (for <em>n</em> ≥ 3). We prove that, for the larger class of pseudolinear drawings, the outer face must be a triangle. The other main result is the next step toward Guy's Conjecture that the crossing number of <em>K<sub>n</sub></em> is $(1/4)[n/2][(n-1)/2][(n-2)/2][(n-3)/2]$. We show that the conjecture is true for <em>n</em> = 11,12; previously the conjecture was known to be true for <em>n</em> ≤ 10. We also prove several minor results.	en
dc.format	application/pdf	en
dc.format.extent	414477 bytes
dc.format.mimetype	application/pdf
dc.identifier.uri	http://hdl.handle.net/10012/1174
dc.language.iso	en	en
dc.pending	false	en
dc.publisher	University of Waterloo	en
dc.rights	Copyright: 2006, Pan, Shengjun. All rights reserved.	en
dc.subject	Mathematics	en
dc.subject	graph	en
dc.subject	crossing number	en
dc.subject	Guy's Conjecture	en
dc.title	On the Crossing Numbers of Complete Graphs	en
dc.type	Master Thesis	en
uws-etd.degree	Master of Mathematics	en
uws-etd.degree.department	Combinatorics and Optimization	en
uws.peerReviewStatus	Unreviewed	en
uws.scholarLevel	Graduate	en
uws.typeOfResource	Text	en

Files

Now showing 1 - 1 of 1